Hybrid feedback controls and stabilization of linear differential systems

We study so-called "hybrid feedback stabilizers" for an arbitrarily general system of linear differential equations. We prove that under assumptions of controllability and observability there exists a hybrid feedback output control which makes the system asymptotically stable. The control is designed by making use of a discrete automation implanted into the system's dynamics. In general, the automation has infinitely many locations, but it gives rise to an "uniform" (in some sense) feedback control. The approach we propose goes back to the classical feedback control technique combined with some ideas used in the stability theory for equations with time-delay.